고체역학 (Gere) — Stresses in Beams (Advanced Topics): Problem 6.5-5

6.5-5 A beam made up of two unequal leg angles is subjected to a bending moment \(M\) having its vector at an angle \(\theta\) to the \(z\) axis (see figure part a). (a) For the position shown in the figure, determine the orientation of the neutral axis and calculate the maximum tensile stress \(\sigma_t\) and maximum compressive stress \(\sigma_c\) in the beam. Assume that \(\theta = 30^\circ\) and \(M = 3.5 \text{ kN}\cdot\text{m}\). (b) The two angles are now inverted and attached back-to-back to form a lintel beam that supports two courses of brick façade (see figure part b). Find the new orientation of the neutral axis and calculate the maximum tensile stress \(\sigma_t\) and maximum compressive stress \(\sigma_c\) in the beam using \(\theta = 30^\circ\) and \(M = 3.5 \text{ kN}\cdot\text{m}\).